prevent z-fighting between billboard particles?
If you would like to avoid Z-fighting you'll need to give your object at lest a small amount of difference in the location for every axis.

I would suggest to slightly increase the Velocity towards the Normal direction (e.g from 0 to 0.01) in order to not alter the overall look of the scene substantially, but at the same time, as each particle raise at different time, you'll have a variable distribution of particle location toward the camera.